EEG electrodes connectivities attempt to simulate a miniature version of the human brain graph. The small hub assumption of the brain graph theory [1]} describes the nerve connections in the human brain as a combination of non-random clustering with short path length. The effect of this assumption is critical in designing brain graph networks as a multi-layered graph structure that propagates information both in the immediate node locality and the deeper neighbourhood. However, past studies have shown that increasing the depth of the GCN converges it to the random walk’s limit distribution [2]}. This inevitably results in information saturation where the hidden states converge to a single point and are skipped in the message passing in deeper layers. The traditional vanilla Graph Convolution (GCN) Layer [3]} is as \( H^{(K+1)}=\sigma \hat{A}H^{(K)}W^{(K)}\) , where \(H^{(K)}\)  and \(H^{(K+1)}\)  are the input and output activation of the layer \(K\) , and \(\hat{A} = D^{-\frac{1}{2}}(A+I_n)D^{-\frac{1}{2}}\)  is a symmetrically normalized adjacency matrix with self-connections. \(W^{(K)}\)  is a trainable weight matrix such that \(W^{(0)}\)  is obtained as output from the AGL layer. The message passing algorithm in GCN acts as a simple neighborhood averaging operator which replaces each row in the feature matrix by the average of its neighbors. Inspired by [4]}, we modify the vanilla GCN layer to introduce the Deep Neighbourhood Graph Convolution (DN-GCN) layer to recursively propagate the neighbourhood information from deep layers selectively over spatially dependent nodes. We modify the vanilla GCN layer with additional inputs from recursively deeper GCN layers to obtain the following equation: \(\scalebox {.9}{\mbox{$\displaystyle H^{K+1}=\sigma (\sum ^{K}_{l=1} \beta _l \hat{A} H^{l}W^l)$}}\) , where \(\beta _l\)  is the depth regularization coefficient selected in a way such that \(\sum ^{K}_{l=1}\beta _l=1\) . This modification retains a proportion of hidden states from each of the previous layers during the propagation step so as to preserve locality and exploring a deeper neighborhood at the same time. However, there can be cases when an EEG electrode node may not have any spatial dependency on its neighbours due to its peripheral location [5]}. To handle such extreme cases, we add a feature selector term, \(S^l\) . For layers that do not have any spatial dependency on the \(l^{th}\)  layer, it is possible that \(S^l=0\) , except for \(l=K\)  to preserve information flowing through the self-connection acquired by the re-normalization trick of vanilla GCN layers. The final representation of the DN-GCN layer is given by \(\scalebox {.9}{\mbox{$\displaystyle H^{K+1}=\sigma (\sum ^{K}_{l=1} \beta _l \hat{A} H^{l}W^l S^l)$}}\) .
